Some colleges had already been moving to eliminate loans from all their financial aid packages and replace them with grants. In the weeks since Harvard’s announcement, a stampede of additional institutions — the University of Pennsylvania, Pomona, Swarthmore, Haverford — have taken the same step, which will help middle- and upper-middle-income families.

But Harvard, in adopting that practice, has also gone far beyond it: for families earning $120,000 to $180,000 a year, costs will now be limited to about 10 percent of income, meaning that students from such families will pay a maximum of $18,000, a deep discount from the university’s full annual cost of more than $45,600.